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Abstract

Objective The Divisive Normalization (DN) function is often viewed as a canonical neural encoding mechanism. However, DN maximizes mutual information, hence efficient, only for input stimuli coming from a long-tail multivariate Pareto distribution. Using behavioral paradigms and computational modeling, we test whether the brain uses DN for choice behavior under diverse distributions of input stimuli, or whether the encoding mechanism varies across different stimulus environments. That is, we ask whether choices are efficiency-constrained by one physiological encoding mechanism or whether the encoding mechanism adapts across different choice environments. We test these hypotheses in a biphasic risky-choice experiment, where subjects were given lotteries from different types of input distributions. Methods In Phase 1, subjects (N=40) reported their willingness-to-pay for participating in a lottery, using a Becker-Degroot-Marschak (1964) auction, aimed at eliciting their risk preferences. The subject-specific risk parameters were used to generate two types of continuous distributions of subjective valuations (SVs): (1) a Uniform distribution, for which the DN encoding function is inefficient; and (2) a multivariate Pareto type-III distribution, for which the DN function is efficient. These distributions were then used in Phase 2 of the study, where subjects made 680 binary choices between pairs of lotteries, half of which were drawn from the Uniform distribution of SVs, whereas the other half were drawn from the Pareto distribution of SVs (counter-balanced across subjects). We used pooled and hierarchical maximum likelihood estimations to recover the DN functional parameters. Results We found that the normalization-weighting factor was significant across the two experimental treatments, in both the pooled and hierarchical estimations. This indicates that subjects employed normalized value encoding regardless of the distribution of the input stimuli they were facing. Nonetheless, the magnitude of the normalization-weighting factor and the curvature of the DN function varied across treatments, suggesting that subjects adapted to the different choice environments. Conclusions Our results suggest that people are obligate DN-choosers, which implies a certain degree of embedded inefficiency in choice. These findings are in line with previous empirical results, showing that many real-world naturalistic stimuli have long-tail asymmetric distributions, and perhaps imply an evolutionary origin of the neural encoding mechanism.